This application incorporates by reference U.S. patent application Ser. No. 12/549,884, entitled Model-Less Inversion-Based Iterative Control Method of Broadband Viscoelasticity Spectroscopy, filed Aug. 28, 2009, U.S. patent application Ser. No. 12/177,215, entitled Model-Less Inversion-Based Iterative Control Algorithm, filed Jul. 22, 2008, and U.S. Provisional Patent Application No. 60/953,313, entitled Model-Less Inversion-Based Iterative Control Algorithm, filed Aug. 1, 2007, the teachings and disclosures of which are incorporated herein in their entireties by reference thereto.
Indentation based approach using scanning probe microscope (SPM) or nanoindenter has become an enabling tool to quantitatively measure the nanomechanical properties of a wide variety of materials, both locally and globally. The current measurement methods, however, are limited in both the frequency range that can be measured and the measurement time that is needed to measure the (frequency) rate dependent viscoelasticity of materials. These limits of current measurement methods, in both measurement frequency and time, arise as the excitation force from the probe to the sample surface employed cannot compensate for the convolution effect of the instrument dynamics, nor rapidly excite the rate-dependent nanomechanical behavior of the material.
Inefficiencies exist in current nanomechanical measurement methods for characterizing the time elapsing properties of soft materials. For example, although nanomechanical properties such as elasticity can be measured by using the force-curve measurements, the excitation input force used is quasi-static and thereby, does not contain rich frequency components to rapidly excite viscoelastic response of materials. One attempt to address the lack of frequency components in the excitation force has been the force modulation technique, where a sinusoidal driven signal (i.e., the input voltage) is applied to the actuator of the cantilever, i.e. piezoelectric actuator, with the aim of generating a sinusoidal excitation force profile. Then the frequency-dependent material properties can be acquired by sweeping the frequency over the measurement frequency range, and measuring the vibration of the probe (the amplitude and the phase) relative to the driving input.
During the measurement, however, the instrument hardware dynamics effect is coupled into the measured data. Although such a coupling effect can be accounted for by modeling the probe-sample interaction dynamics as a spring-mass-damper system, the model is adequate only for the low frequency range, whereas large measurement errors occur as the dynamics model becomes more complicated and erroneous when the measurement frequency becomes high (relative to the hardware bandwidth). Moreover, the force-modulation technique is slow to sweep a large frequency range as the de-modulation process involved is inherently time consuming. The measurement time can be reduced by using the recently-developed multi-frequency method. However, the frequency components used are not optimized, and the measurement frequency range is still limited by the instrument dynamics convolution effect. Evidently, there is a need to improve the current indentation-based nanomechanical property measurement methods.
One of the main challenges to achieve rapid broadband nanomechanical measurement is to ensure that 1) the force applied shall accurately track the desired force profile and 2) the indentation should be accurately measured. Accurate tracking of the desired force profile is necessary to excite the material behavior in the measured frequency range, as well as to avoid issues related to low signal-to-noise ratio and input saturation (due to the force being too small or too large). Accurate indentation measurement is needed to capture (and only capture) the material behavior as the response to the force applied. When the measurement frequency range becomes large (i.e., broadband), however, the dynamics of the system consisting of the piezoactuator and the probe can be excited, resulting in large vibrations of the probe relative to the sample. Furthermore, substantial dynamics uncertainties exist in the SPM system due to the thermal drift and the change of operation condition (e.g., change of the probe). Additional force tracking errors can also be generated when the displacement of the piezoactuator is large and as a result, the hysteresis effect of the piezoactuator becomes pronounced.
These adverse effects on the excitation force can be mitigated by using control techniques so that the excitation force can be accurately exerted onto the sample surface, as demonstrated recently by using the iterative learning control methods. Residual instrument dynamics effect, however, still exists in the indentation measured (as the indentation is measured indirectly from the difference between the probe response on the soft sample to be measured and that on a hard reference sample). Recently, model based techniques have been developed to account for the dynamics convolution effect on the measured indentation data. These post-processing techniques, however, cannot be used to achieve rapid broadband nanomechanical measurements, as discussed next.
The other major challenge in rapid broadband nanomechanical measurements is to achieve rapid excitation of the material response by the force applied (from the probe). Rapid excitation (of the material response) is needed to capture the time-elapsing nanomechanical properties during dynamic evolution of the material, for example, during the initial rapid stage of the crystallization of polymers or the healing process of live cell. Moreover, rapid excitation of material response is also needed when mapping the nanomechanical properties of the material over the sample surface.
Although the mapping of elasticity/stiffness of materials at nanoscale can be obtained by using the force volume mapping technique, the force-curve measured at each sample point is quasi-static and the mapping procedure is time consuming, with mapping time in tens of minutes to several hours, which becomes even much longer to map rate-dependent nanomechanical properties. Such a long mapping time renders the adverse effects due to disturbances (e.g., thermal drift) and variations of system dynamics pronounced. As a result, large measurement errors occur, particularly when the sample is evolving. Recently, a frequency-rich excitation force with power spectrum similar to band-limited white noise has been utilized for broadband nanomechanical measurement. Although the iterative learning control (ILC) technique has been applied for the tracking of such a complicated desired trajectory, dynamics convolution effect discussed above still exists. Thus, both the above two major challenges in rapid broadband nanomechanical measurements are closely related to the excitation force applied.